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A030119
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a(n) = a(n-1) + a(n-2) + n
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3
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1, 1, 4, 8, 16, 29, 51, 87, 146, 242, 398, 651, 1061, 1725, 2800, 4540, 7356, 11913, 19287, 31219, 50526, 81766, 132314, 214103, 346441, 560569, 907036, 1467632, 2374696, 3842357, 6217083, 10059471, 16276586, 26336090, 42612710, 68948835
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..400
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FORMULA
| Periodic mod 6.
G.f. [1-2x+3x^2-x^3]/[(1-x-x^2)(1-x)^2].
Lucas(n+2) + Fibonacci(n+1) - (n+3).
a(0)=1, a(1)=1, a(2)=4, a(3)=8, a(n)=3*a(n-1)-2*a(n-2)-a(n-3)+a(n-4) [From Harvey P. Dale, Nov 06 2011]
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MATHEMATICA
| RecurrenceTable[{a[0]==a[1]==1, a[n]==a[n-1]+a[n-2]+n}, a, {n, 40}] (* or *) LinearRecurrence[{3, -2, -1, 1}, {1, 1, 4, 8}, 40] (* From Harvey P. Dale, Nov 06 2011 *)
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PROG
| (MAGMA) [Lucas(n+2) + Fibonacci(n+1) - (n+3) : n in [0..40]]; // Vincenzo Librandi, Nov 16 2011
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CROSSREFS
| Sequence in context: A050856 A128441 A009861 * A034451 A099992 A053163
Adjacent sequences: A030116 A030117 A030118 * A030120 A030121 A030122
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KEYWORD
| nonn,easy
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AUTHOR
| Dragan Stevanovic (dragance(AT)ban.junis.ni.ac.yu)
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EXTENSIONS
| Description corrected and sequence extended by Erich Friedman (erich.friedman(AT)stetson.edu).
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